Optimality of tree-type control hierarchy for a symmetric production line

A model of a multilayer hierarchy controlling a “production line”, i. e., a business process with workers interacting sequentially with the same intensity, is considered. Manager's costs are described by a power function dependent on the intensity of the sub-process controlled by the manager. The paper proves that the optimal tree-type hierarchy is the one for which the search is reduced to a constrained optimization problem. The optimal tree for a convex cost function is derived analytically.